A phase transformation can occur when a system has an accessible state of lower
free energy. The mechanism of the transformation is critically dependent
on whether the starting state is metastable or unstable.

An unstable system can transform by making changes that are small
in degree but large in extent. Such situations lead to mechanisms that are
called continuous transformations. The main categories of continuous
transformations in materials are spinodal decomposition and
continuous ordering.

A metastable system can transform by making changes that are large
in degree but small in extent. Such situations require
nucleation of the
new phase. After nucleation takes place, a new particle can grow
until it either
impinges with another particle, or supersaturation of the surrounding material
is depleted.

First-order and second-order transitions

Ehrenfest proposed a useful scheme for classification of phase
transformations based on discontinuities in derivatives of the free
energy function that are characteristic of the transformation.
Simply put, the order or a phase transformation is the lowest
order of the derivative of that shows a discontinuity.

Examples: melting; ordering in brass

Decomposition into Phases: Conserved Fields

Figure 27-1:
Decomposition requires long-rang diffusion.
Such a transformation requires flux of a conserved field, like
composition , which
has an integral that is conserved for a closed system.

Order-Disorder: Nonconserved Fields

Figure 27-2:
The phase change does not
require long-rang diffusion.
Such a transformation involves local changes in some field, like the
order parameter , which
is not conserved for a closed system.